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The number of distinct prime divisors of the number 512^3 - 253^3 - 259^3 is

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KVPY Other Question

Three circles each of radius 1, touch one another externally and they lie between two parallel lines. The minimum possible distance between the lines is Consider an incomplete pyramid of balls on a square base having 18 layers; and having 13 balls on each side of the top layer. Then the total number N of balls in that pyramid satisfies
option
(A) 9000 < N < 10000
(B) 8000 < N < 9000
(C) 7000 < N < 8000
(D) 10000 < N < 12000